It pretty much reiterates what you said. But leads to more questions from me (a layman). For example, the second quote above: it seems to be ysaying that the gravity created by the mass was created by gravity. (And, by-the-way, why, after the Big Bang was matter unevenly dispersed?
Getting back to the topic, I suppose the "missing link" they are searching for could be said to be the manner in which "gravity causing matter to clump" eventually led to organic life (and, apparently, only on planet Earth).
Gravity and mass and every other aspect of the Universe developed during and immediately after the Big Bang. The word “created” is as good as any. Mathematicians and physicists have spent entire careers trying to sort out the dynamics of that event, and there are still more questions than ever about how it all worked.
But to answer your question about why the uneven distribution - It’s because it is impossible for so much mass to be perfectly evenly distributed. The early universe had all the mass it has now packed into a really small space. Practically infinite numbers of collisions and interactions occurring simultaneously will always cause some areas to have more particles and some to have less, and that is all it takes for the process to start.
As for the “missing link” you are on the right track. The Big Bang events and the transition from chemical reactions to life forming are two areas that today’s science and technology have not yet solved. I believe it may be possible in the near future to use supercomputers to model the chemical interactions and chemistry necessary to form the first living things.
There are already simulations and actual chemistry experiments that have resulted in production of cellular membranes, amino acids and nucleic acids.